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I have a collection of sixteen cards. Each card is rose, amber, emerald, or liberty (a shade of blue) . Also, each card is labelled A, B, C, or D. There is a card for each color-letter combination, e.g. there is an amber card that has a B on it.

These sixteen cards are dealt at random to four people, and each person gets four cards. What is the probability that each person gets a card with a letter A on it?

 

urgent pls help!

 Dec 2, 2019
 #1
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We can use a constructive approach, which isolates the unique probabilities for each card.  This gives us an answer of (1/16*c(16,1) + 1/15*c(16,2) + 1/14*c(16,3) + 1/13*c(16,4))/c(16,4) = 27/260.

 
 Dec 2, 2019
 #2
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I'm getting a different answer: The probability is 4/16*3/15*2/14*1/13 = 1/1820.

 
 Dec 3, 2019
 #3
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If we choose the multi-event spectrums, such as rose, rose plus amber, rose plus amber plus emerald, and all possible 2^4 = 16 choices, we'll get a probability of 4/16 - c(4,3)*3/16*15 + c(4,2)*2/16*15*14 - c(4,1)*1/16*15*14*13, which works out to 2/15.

 
 Dec 4, 2019

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